Local Projections Are VAR Predictions of Increasing Order

Abstract

This paper explores local projections (LPs) and vector autoregressions (VARs), two important time series models in economics. I prove that LPs can be represented as combinations of equal and higher-order VARs, while VARs themselves are combinations of equal and lower-order LPs. This finding advances our understanding of LPs and VARs and leads to enhanced efficiency and model selection. Key contributions include: (i) enhancing model selection by comparing LPs and VARs that are equally parsimonious; (ii) improving the efficiency of LP estimation by leveraging the underlying VAR structure; and (iii) introducing the VAR sequence (VAR-S), a new empirical model that unifies LPs and VARs, thereby stimulating new avenues for research and advancements in the field.

Keywords: Impulse Response Function, Multistep Forecasting, Local Projection, Vector Autoregression, VAR Sequence